TY - JOUR
T1 - Mean Field Analysis of Quantum Annealing Correction
AU - Matsuura, Shunji
AU - Nishimori, Hidetoshi
AU - Albash, Tameem
AU - Lidar, Daniel A.
N1 - Funding Information:
S.M. and H.N. thank Y. Seki for his useful comments. D.A.L. and T.A. acknowledge support under ARO Grant No. W911NF-12-1-0523, ARO MURI Grant No. W911NF-11-1-0268, NSF Grant No. CCF-1551064, and partial support from Fermi Research Alliance, LLC under Contract No. DE-AC02-07CH11359 with the United States Department of Energy. H.N. acknowledges support by JSPS KAKENHI Grant No. 26287086.
Publisher Copyright:
© 2016 American Physical Society.
PY - 2016/6/1
Y1 - 2016/6/1
N2 - Quantum annealing correction (QAC) is a method that combines encoding with energy penalties and decoding to suppress and correct errors that degrade the performance of quantum annealers in solving optimization problems. While QAC has been experimentally demonstrated to successfully error correct a range of optimization problems, a clear understanding of its operating mechanism has been lacking. Here we bridge this gap using tools from quantum statistical mechanics. We study analytically tractable models using a mean-field analysis, specifically the p-body ferromagnetic infinite-range transverse-field Ising model as well as the quantum Hopfield model. We demonstrate that for p=2, where the phase transition is of second order, QAC pushes the transition to increasingly larger transverse field strengths. For p≥3, where the phase transition is of first order, QAC softens the closing of the gap for small energy penalty values and prevents its closure for sufficiently large energy penalty values. Thus QAC provides protection from excitations that occur near the quantum critical point. We find similar results for the Hopfield model, thus demonstrating that our conclusions hold in the presence of disorder.
AB - Quantum annealing correction (QAC) is a method that combines encoding with energy penalties and decoding to suppress and correct errors that degrade the performance of quantum annealers in solving optimization problems. While QAC has been experimentally demonstrated to successfully error correct a range of optimization problems, a clear understanding of its operating mechanism has been lacking. Here we bridge this gap using tools from quantum statistical mechanics. We study analytically tractable models using a mean-field analysis, specifically the p-body ferromagnetic infinite-range transverse-field Ising model as well as the quantum Hopfield model. We demonstrate that for p=2, where the phase transition is of second order, QAC pushes the transition to increasingly larger transverse field strengths. For p≥3, where the phase transition is of first order, QAC softens the closing of the gap for small energy penalty values and prevents its closure for sufficiently large energy penalty values. Thus QAC provides protection from excitations that occur near the quantum critical point. We find similar results for the Hopfield model, thus demonstrating that our conclusions hold in the presence of disorder.
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U2 - 10.1103/PhysRevLett.116.220501
DO - 10.1103/PhysRevLett.116.220501
M3 - Article
AN - SCOPUS:84973483652
VL - 116
JO - Physical Review Letters
JF - Physical Review Letters
SN - 0031-9007
IS - 22
M1 - 220501
ER -